A function $f$ is said to be continuous at a point $c$ if it satisfies three properties:

  1. Should be defined at the point $c$
  2. Left and right-hand limits at $c$ must be equal i.e., the limit must exist
  3. Limit value at point $c$ is equal to the actual value of the function at c

In short: $\lim \limits_{x \rightarrow c} f(x) = f(c)$

I want to know whether the functions that we want to learn through real-world data, say generator in GAN, such as images, audio, video, text corpora, etc., are continuous or highly discontinuous in general? If discontinuous, what might be the reason for discontinuity? I mean, which among the three properties mentioned got a violation in the majority of cases?

  • 1
    $\begingroup$ As said in the description, discontinuity is a property of the function. So, we can't talk of it just by looking at the data. It all depends on what kind of function to define over it. $\endgroup$
    – SpiderRico
    Aug 22 at 1:41
  • $\begingroup$ @SpiderRico I mean suppose I want to learn a generator, Then the function is the function of generator neural network... $\endgroup$
    – hanugm
    Aug 22 at 1:45
  • $\begingroup$ @SpiderRico so are you saying to narrow down the function I want to simulate? $\endgroup$
    – hanugm
    Aug 22 at 1:46

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